COUPLED LONGITUDINAL MODULATIONAL INSTABILITY OF ELECTRON-CYCLOTRON WAVES

The modulational instability of an electron cyclotron wave is studied for single and double pump systems. For both cases, the maximum growth rates of modulational instability are reduced by the velocity mismatc h caused by the time dependent ponderomotive force. The thresholds for absolute modulational instability are numerically obtained by way of the impulse response curve. The threshold for the absolute modulationa l instability of a copropagating high frequency electron cyclotron wav e is lowered by the time dependent ponderomotive force. Also, the modu lational instabilities of copropagating whistler waves are always conv ective since the velocity mismatch caused by the time dependent ponder omotive force is very large. In the case of counterpropagating pumps, the modulational instabilities are always absolute no matter how large the ratios of the pump intensities are. In a coupled pump system, the contribution of the time dependent ponderomotive force is greater tha n that for the case of a single pump system.